Tension Increases Teriparatide-Induced Bone Formation More Than Compression in the Human Femoral Neck

Amanda M. Rooney1, Mathias P.G. Bostrom2, David W. Dempster3,4, Jeri W. Nieves3,4, Hua Zhou3, Marsha Zion3, Catherine Roimisher3, Yvonne Houle2, Felicia Cosman3,4

1Cornell University, Ithaca, NY, 2Hospital for Special Surgery, New York, NY, 3Helen Hayes Hospital, West Haverstraw, NY, 4Columbia University, New York, NY

Disclosures: Amanda M. Rooney (N), Mathias P.G. Bostrom (N), David W. Dempster (2-Eli Lilly), Jeri W. Nieves (N), Hua Zhou (N), Marsha Zion (N), Catherine Roimisher (N), Yvonne Houle (N), Felicia Cosman (2-Eli Lilly) Introduction: Most treatments for osteoporosis, such as bisphosphonates, preserve existing bone by inhibiting bone remodeling1. Parathyroid hormone (PTH) and its analogs, including teriparatide (TPTD), provide an alternative mechanism. TPTD increases the remodeling rate and the amount of bone formed during each remodeling cycle1. Iliac crest biopsies have demonstrated that PTH increases cortical and cancellous bone formation in humans2-3. To more fully understand the mechanisms behind PTH-related treatments, dynamic histomorphometric analysis has been used to measure cellular activity and the rates at which they occur2-3. New bone is marked by fluorescent labels that are integrated into forming bone. By providing two doses to patients over a known time interval, the rate of formation and the extent of formation over that time period can be determined. Because this method requires the administration of these labels to a live subject, biopsy tissue has been the main source of data, limiting the site of analysis. While mechanical loading may amplify the benefits of PTH4-6, little is known about how the type of mechanical loading influences its role. No study to date has compared PTH treatment under tensile versus compressive loading in humans. The femoral neck is subject to bending7, thereby providing a unique opportunity to study tensile and compressive loading at a single anatomical site from the same subject. Total hip replacements (THR) offer an ethical platform to obtain labeled femoral neck tissue. This study aimed to demonstrate a difference in histomorphometric indices between the tensile and compressive sides of the human femoral neck with TPTD treatment. Methods: This study was approved by the Institutional Review Boards of Hospital for Special Surgery and Helen Hayes Hospital. All subjects gave informed consent. Thirty-eight postmenopausal men and women aged 60-89 with severe hip osteoarthritis requiring THR were randomized into two treatment groups, TPTD (n=21) and placebo (PBO) (n=17). Demographics were not different between the two groups. Treatments consisted of 20 µg of TPTD or identically appearing placebo, and were administered subcutaneously on a daily basis for an average of 6 weeks (range 4.6-11.8 weeks). Preoperative fluorescent labels were administered 4 times daily on the following schedule: 250 mg tetracycline for 3 days, 10 days off, 150 mg demeclocycline for 3 days, and 5-10 days off before THR. During surgery, a section of the femoral neck was removed then later fixed, sectioned, and stained with toluidine blue or mounted unstained as previously described2. The samples were divided into octants following the protocol established by Bell et al8 (Fig. 1). Superior (S) and superior-posterior (S-P) octants were categorized as tensile, and inferior (I) and inferior-anterior (I-A) octants were categorized as compressive. The endocortical (Ec) and periosteal (Ps) surfaces were analyzed for mineral apposition rate (MAR), mineralized surface (MS/BS), number of osteoclasts (Oc.N/BS), and eroded surface (ES/BS). Data are presented as mean ± SEM. Comparisons between tensile and compressive data within a treatment group were evaluated using a paired t-test, and comparisons between treatment groups within a mechanical loading environment were evaluated using a two-sample t-test assuming equal variances. Significance was defined by a p-value of less than 0.05. Data with matching letters are statistically significantly different. Results: Dynamic histomorphometric indices were compared across loading condition and treatment group. Ec-MS/BS and Oc.N/BS were greater on the tensile side than the compressive side in the TPTD group but not in the PBO group (Fig. 2). Ec-MS/BS also increased with TPTD treatment on the compressive side, and just missed significance on the tensile side (p=0.058). Ec-ES/BS showed no significant change across treatment and loading condition, although there was a trend toward greater values on the compressive side in the PBO group (p=0.08). Ps-MS/BS was greater on the compressive side than the tensile side for the PBO group but not for the TPTD group (Fig. 2). Ec- and Ps-MAR were similar across treatment and loading condition. Discussion: TPTD treatment affected the tensile and compressive sides of the femoral neck differently. Within the Ec surface, TPTD led to greater values of MS/BS and Oc.N/BS on the tensile side than the compressive side. Within the Ps surface, the difference in MS/BS present in the PBO group was equalized with TPTD. This effect was most likely due to an increase on the tensile side even though statistical significance was not reached (p=0.12 tensile, p=0.92 compressive). All three of these measurements indicate that TPTD causes a greater increase of cortical bone formation parameters under tension than under compression. Data from four-point bending in rat tibiae with PTH showed similar increases in new bone formation to our results5-6, with Ps formation suggesting greater increases in regions of tension5. Our data show that TPTD changes the extent of bone forming surfaces rather than the rate of matrix apposition on the Ec and Ps surfaces in the human femoral neck, and leads to greater stimulation of bone formation on the tensile cortex than the compressive cortex. Significance: Our study revealed that tensile and compressive loads influence TPTD differently. This knowledge furthers our mechanistic understanding of TPTD, and will help lead to future osteoporosis treatment plans that take advantage of the synergistic effects of mechanical loading and TPTD. Acknowledgements: We thank Eli Lilly for supplying TPTD and PBO. Funding was provided by NIAMS R01-ARO59204. References: [1] Hodsman et al Endocr Rev 2005. [2] Dempster et al JBMR 2001. [3] Lindsay et al JBMR 2007. [4] Kim et al JBMR 2003. [5] Hagino et al JBMM 2001. [6] Roberts et al J Biomech 2009. [7] Nawathe et al J Biomech 2015. [8] Bell et al JBMR 1999.

Figure 1: Division into octants.

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4. Discussion

These results elucidate how the overall load is shared betweenthe cortical and trabecular bone in the elderly human femoralneck. We found that while the cortical bone supported up to 90%of the overall frontal-plane bending moment in stance loading, itsupported only about 60% in sideways fall loading, indicating theimportant role of trabecular bone for the latter. A region ofuniform load-sharing consistently occurs in the distal portion ofthe femoral neck, and extended over a greater length of the neckfor the sideways fall loading than for the stance loading. Whiledistally the cortical bone was most highly stressed, proximally itwas the trabecular bone that experienced the highest stresses.Comparing the finite element-estimated tissue-level axial displa-cements along the inferior–superior axis in the distal neck withthe Euler beam theory-based predictions indicated that the distalneck does not exhibit a classic beam-type bending behavior. Thissuggests that simple engineering models, such as the Euler beamtheory, may not be applicable for simulating stress distributionwithin the femur and thus for computing cortical or trabecularload-fraction in the femoral neck. Taken together, by demonstrat-ing well-delineated, consistent regions of uniform load-sharingand load-transfer between the cortical and trabecular bone, thisstudy demonstrates the different biomechanical characteristics of

the proximal and distal portions of the neck, and elucidates themechanisms by which high stresses can develop in the cortical ortrabecular bone tissue in the neck.

Fig. 4. The variation in the distribution of tissue-level axial stress across thefemoral neck cross-sections, for sideways fall and stance loading cases, for a singlefemur. S: Superior, P: Posterior, A: Anterior, I: Inferior.

Fig. 5. The variation in tissue-level axial displacement along the inferior–superioraxis of a distal cross-section of the femoral neck, as predicted using finite elementcomputations and Euler beam theory, for a sideways fall loading (top) and stanceloading (bottom), for a single femur. S: Superior, I: Inferior. g: gradient of axialdisplacement (mm/# of data points) in the cortical bone. All the data points areuniformly distanced within the cortical region. The colored plots representdistributions of tissue-level axial stress, as shown in Fig. 4.

Fig. 3. The variation in the fraction of total frontal-plane bending moment carriedby the cortical bone for: (a) a sideways fall loading; and (b) stance loading. Thevertical dotted line indicates the transition from the uniform load-sharing region tothe load-transfer region. Error bars represent standard deviations from the meanvalues (for n¼18 bones). X¼0 corresponds to the most distal plane of thefemoral neck.

S. Nawathe et al. / Journal of Biomechanics 48 (2015) 816–822 819

Sample

model the cortical width data in the frequency domain.Modeling cortical widths takes account of the subject varia-tion, as well as location, biopsy type (i.e., fracture or con-trol), and gender. It was postulated that modeling in thefrequency domain would make it possible to mathemati-cally predict cortical widths at any location in the femoralneck. A model with fewer independent variates (i.e., fewerthan 128 separate width measurements) has equal orgreater power to achieve between-group separation at spe-cific locations within the femoral neck cortex.

The circumferential distribution of cortical widths in boththe control (male or female) and fracture (complete or in-complete) groups were modeled using the JMP statisticalpackage. To normalize the distribution of residuals, thesquare root of the cortical width (dependent variable) wasadopted. Least squares regression models used (1) a simpleFourier series, periodic functions of the measurement angle(sin angle + cos angle, sin 2� angle + cos 2� angle, sin 3�angle + cos 3� angle, sin 4� angle + cos 4� angle, sin 6�angle + cos 6� angle, sin 8� angle + cos 8� angle, sin 9�angle + cos 9� angle), or (2) the 128 width measurements asindependent categorical variables. For both models, subjectand gender or disease were used as independent categoricalvariables, and disease or gender were modeled as an inter-action with the angular location of width. Comparison ofthese two models demonstrated that the model with 128independent widths measurements improved the goodnessof fit, but because it increased the numbers of degrees of

freedom assigned to the model this improvement was notstatistically significant in the comparison for the effect ofgender (p 4 0.071) or for that of disease (p 4 0.94). Fromthe first (frequency domain) model the circumferential dis-tribution of cortical widths was predicted (with 95% confi-dence intervals [CIs]) for each subject group.

RESULTSSubjects

For the control subjects, there were no significant differ-ences between the males and females in their ages (p >0.75). Time since death was also unrelated to the amountsof cortical or cancellous bone (p > 0.21). There was nosignificant difference in the ages of the female fracture andfemale control groups (p > 0.21). In the female fracturegroup, there was no association between time since fractureand the amounts of cortical (p > 0.44) or cancellous bone (p> 0.93).

Total bone area

In the control samples, male subjects had a significantlygreater maximum (male 34.32 ± 0.79 mm, female 30.76 ±0.55; p 4 0.0016) and minimum (male 29.66 ± 1.13, female24.52 ± 0.61; p 4 0.0012) cross-section diameter. However,there were no differences in these dimensions between thefemale control and the female fracture group (fracture:maximum 31.67 ± 1.08, p 4 0.503; minimum 25.64 ± 0.72, p4 0.271). The ratio of maximum to minimum diameterswas not different between fractures and controls (fractures:1.25 ± 0.04; female controls 1.26 ± 0.03, male controls 1.16± 0.04; p > 0.05 Tukey–Kramer HSD test).

Six of the 13 biopsies from the fracture cases had sub-stantial proportions of the posterior and inferoposterior re-gions missing, with the other regions being intact. Therewere no differences in the maximum and minimum diam-eters between the complete and incomplete biopsies nor inthe ratio of these diameters (p > 0.635). The proportion ofsubcapital (n 4 5) and transcervical (n 4 1) fractures wasnot significantly different from that in the group of com-plete biopsies (p 4 0.31, Chi-square analysis).

The total bone area of the whole cross-section in thecontrol group showed that males had significantly morebone than females (males 227.55 ± 14.9 mm2; females 184.8± 6.83 mm2; p 4 0.015). Although total bone area waslower in samples from femoral neck fractures than femalecontrols, this was not significant (fractures 165.85 ± 10.08; p4 0.159). However, when the total amount of bone wasexpressed as a proportion of bone + marrow, it was signifi-cantly reduced in the fracture group (Tt.Ar: female fracture27.83 ± 1.18%, female control 33.62 ± 1.47%; p 4 0.0054;male control 30.81 ± 2.23). In the control group, there wereno differences in the Tt.Ar (%) between females and males(p 4 0.298). There were no differences in either the totalbone area or the Tt.Ar (%) between the complete andincomplete biopsies from the fracture group.

FIG. 1. Schematic cross-section of the femoral neck show-ing the eight regions used for the segmental analysis. Re-gions: I, inferior; I-A, inferoanterior; A, anterior; S-A, su-peroanterior; S, superior; S-P, superoposterior; P, posterior;and I-P, inferoposterior.

BELL ET AL.114

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Figure 1: Samples were divided into octants. Tensile is superior, superior-posterior (S, S-P). Compressive is inferior, inferior-anterior (I, I-A).

Figure 2: Dynamic histomorphometric indices presented as mean ± SEM. Matching letters denote significance with p<0.05.

model the cortical width data in the frequency domain.Modeling cortical widths takes account of the subject varia-tion, as well as location, biopsy type (i.e., fracture or con-trol), and gender. It was postulated that modeling in thefrequency domain would make it possible to mathemati-cally predict cortical widths at any location in the femoralneck. A model with fewer independent variates (i.e., fewerthan 128 separate width measurements) has equal orgreater power to achieve between-group separation at spe-cific locations within the femoral neck cortex.

The circumferential distribution of cortical widths in boththe control (male or female) and fracture (complete or in-complete) groups were modeled using the JMP statisticalpackage. To normalize the distribution of residuals, thesquare root of the cortical width (dependent variable) wasadopted. Least squares regression models used (1) a simpleFourier series, periodic functions of the measurement angle(sin angle + cos angle, sin 2� angle + cos 2� angle, sin 3�angle + cos 3� angle, sin 4� angle + cos 4� angle, sin 6�angle + cos 6� angle, sin 8� angle + cos 8� angle, sin 9�angle + cos 9� angle), or (2) the 128 width measurements asindependent categorical variables. For both models, subjectand gender or disease were used as independent categoricalvariables, and disease or gender were modeled as an inter-action with the angular location of width. Comparison ofthese two models demonstrated that the model with 128independent widths measurements improved the goodnessof fit, but because it increased the numbers of degrees of

freedom assigned to the model this improvement was notstatistically significant in the comparison for the effect ofgender (p 4 0.071) or for that of disease (p 4 0.94). Fromthe first (frequency domain) model the circumferential dis-tribution of cortical widths was predicted (with 95% confi-dence intervals [CIs]) for each subject group.

RESULTSSubjects

For the control subjects, there were no significant differ-ences between the males and females in their ages (p >0.75). Time since death was also unrelated to the amountsof cortical or cancellous bone (p > 0.21). There was nosignificant difference in the ages of the female fracture andfemale control groups (p > 0.21). In the female fracturegroup, there was no association between time since fractureand the amounts of cortical (p > 0.44) or cancellous bone (p> 0.93).

Total bone area

In the control samples, male subjects had a significantlygreater maximum (male 34.32 ± 0.79 mm, female 30.76 ±0.55; p 4 0.0016) and minimum (male 29.66 ± 1.13, female24.52 ± 0.61; p 4 0.0012) cross-section diameter. However,there were no differences in these dimensions between thefemale control and the female fracture group (fracture:maximum 31.67 ± 1.08, p 4 0.503; minimum 25.64 ± 0.72, p4 0.271). The ratio of maximum to minimum diameterswas not different between fractures and controls (fractures:1.25 ± 0.04; female controls 1.26 ± 0.03, male controls 1.16± 0.04; p > 0.05 Tukey–Kramer HSD test).

Six of the 13 biopsies from the fracture cases had sub-stantial proportions of the posterior and inferoposterior re-gions missing, with the other regions being intact. Therewere no differences in the maximum and minimum diam-eters between the complete and incomplete biopsies nor inthe ratio of these diameters (p > 0.635). The proportion ofsubcapital (n 4 5) and transcervical (n 4 1) fractures wasnot significantly different from that in the group of com-plete biopsies (p 4 0.31, Chi-square analysis).

The total bone area of the whole cross-section in thecontrol group showed that males had significantly morebone than females (males 227.55 ± 14.9 mm2; females 184.8± 6.83 mm2; p 4 0.015). Although total bone area waslower in samples from femoral neck fractures than femalecontrols, this was not significant (fractures 165.85 ± 10.08; p4 0.159). However, when the total amount of bone wasexpressed as a proportion of bone + marrow, it was signifi-cantly reduced in the fracture group (Tt.Ar: female fracture27.83 ± 1.18%, female control 33.62 ± 1.47%; p 4 0.0054;male control 30.81 ± 2.23). In the control group, there wereno differences in the Tt.Ar (%) between females and males(p 4 0.298). There were no differences in either the totalbone area or the Tt.Ar (%) between the complete andincomplete biopsies from the fracture group.

FIG. 1. Schematic cross-section of the femoral neck show-ing the eight regions used for the segmental analysis. Re-gions: I, inferior; I-A, inferoanterior; A, anterior; S-A, su-peroanterior; S, superior; S-P, superoposterior; P, posterior;and I-P, inferoposterior.

BELL ET AL.114

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Figure 1: Samples were divided into octants. Tensile is superior, superior-posterior (S, S-P). Compressive is inferior, inferior-anterior (I, I-A).

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Figure 2: Data presented as mean ± SEM. Matching letters denote significance with p<0.05.

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4. Discussion

These results elucidate how the overall load is shared betweenthe cortical and trabecular bone in the elderly human femoralneck. We found that while the cortical bone supported up to 90%of the overall frontal-plane bending moment in stance loading, itsupported only about 60% in sideways fall loading, indicating theimportant role of trabecular bone for the latter. A region ofuniform load-sharing consistently occurs in the distal portion ofthe femoral neck, and extended over a greater length of the neckfor the sideways fall loading than for the stance loading. Whiledistally the cortical bone was most highly stressed, proximally itwas the trabecular bone that experienced the highest stresses.Comparing the finite element-estimated tissue-level axial displa-cements along the inferior–superior axis in the distal neck withthe Euler beam theory-based predictions indicated that the distalneck does not exhibit a classic beam-type bending behavior. Thissuggests that simple engineering models, such as the Euler beamtheory, may not be applicable for simulating stress distributionwithin the femur and thus for computing cortical or trabecularload-fraction in the femoral neck. Taken together, by demonstrat-ing well-delineated, consistent regions of uniform load-sharingand load-transfer between the cortical and trabecular bone, thisstudy demonstrates the different biomechanical characteristics of

the proximal and distal portions of the neck, and elucidates themechanisms by which high stresses can develop in the cortical ortrabecular bone tissue in the neck.

Fig. 4. The variation in the distribution of tissue-level axial stress across thefemoral neck cross-sections, for sideways fall and stance loading cases, for a singlefemur. S: Superior, P: Posterior, A: Anterior, I: Inferior.

Fig. 5. The variation in tissue-level axial displacement along the inferior–superioraxis of a distal cross-section of the femoral neck, as predicted using finite elementcomputations and Euler beam theory, for a sideways fall loading (top) and stanceloading (bottom), for a single femur. S: Superior, I: Inferior. g: gradient of axialdisplacement (mm/# of data points) in the cortical bone. All the data points areuniformly distanced within the cortical region. The colored plots representdistributions of tissue-level axial stress, as shown in Fig. 4.

Fig. 3. The variation in the fraction of total frontal-plane bending moment carriedby the cortical bone for: (a) a sideways fall loading; and (b) stance loading. Thevertical dotted line indicates the transition from the uniform load-sharing region tothe load-transfer region. Error bars represent standard deviations from the meanvalues (for n¼18 bones). X¼0 corresponds to the most distal plane of thefemoral neck.

S. Nawathe et al. / Journal of Biomechanics 48 (2015) 816–822 819

Sample

model the cortical width data in the frequency domain.Modeling cortical widths takes account of the subject varia-tion, as well as location, biopsy type (i.e., fracture or con-trol), and gender. It was postulated that modeling in thefrequency domain would make it possible to mathemati-cally predict cortical widths at any location in the femoralneck. A model with fewer independent variates (i.e., fewerthan 128 separate width measurements) has equal orgreater power to achieve between-group separation at spe-cific locations within the femoral neck cortex.

The circumferential distribution of cortical widths in boththe control (male or female) and fracture (complete or in-complete) groups were modeled using the JMP statisticalpackage. To normalize the distribution of residuals, thesquare root of the cortical width (dependent variable) wasadopted. Least squares regression models used (1) a simpleFourier series, periodic functions of the measurement angle(sin angle + cos angle, sin 2� angle + cos 2� angle, sin 3�angle + cos 3� angle, sin 4� angle + cos 4� angle, sin 6�angle + cos 6� angle, sin 8� angle + cos 8� angle, sin 9�angle + cos 9� angle), or (2) the 128 width measurements asindependent categorical variables. For both models, subjectand gender or disease were used as independent categoricalvariables, and disease or gender were modeled as an inter-action with the angular location of width. Comparison ofthese two models demonstrated that the model with 128independent widths measurements improved the goodnessof fit, but because it increased the numbers of degrees of

freedom assigned to the model this improvement was notstatistically significant in the comparison for the effect ofgender (p 4 0.071) or for that of disease (p 4 0.94). Fromthe first (frequency domain) model the circumferential dis-tribution of cortical widths was predicted (with 95% confi-dence intervals [CIs]) for each subject group.

RESULTSSubjects

For the control subjects, there were no significant differ-ences between the males and females in their ages (p >0.75). Time since death was also unrelated to the amountsof cortical or cancellous bone (p > 0.21). There was nosignificant difference in the ages of the female fracture andfemale control groups (p > 0.21). In the female fracturegroup, there was no association between time since fractureand the amounts of cortical (p > 0.44) or cancellous bone (p> 0.93).

Total bone area

In the control samples, male subjects had a significantlygreater maximum (male 34.32 ± 0.79 mm, female 30.76 ±0.55; p 4 0.0016) and minimum (male 29.66 ± 1.13, female24.52 ± 0.61; p 4 0.0012) cross-section diameter. However,there were no differences in these dimensions between thefemale control and the female fracture group (fracture:maximum 31.67 ± 1.08, p 4 0.503; minimum 25.64 ± 0.72, p4 0.271). The ratio of maximum to minimum diameterswas not different between fractures and controls (fractures:1.25 ± 0.04; female controls 1.26 ± 0.03, male controls 1.16± 0.04; p > 0.05 Tukey–Kramer HSD test).Six of the 13 biopsies from the fracture cases had sub-

stantial proportions of the posterior and inferoposterior re-gions missing, with the other regions being intact. Therewere no differences in the maximum and minimum diam-eters between the complete and incomplete biopsies nor inthe ratio of these diameters (p > 0.635). The proportion ofsubcapital (n 4 5) and transcervical (n 4 1) fractures wasnot significantly different from that in the group of com-plete biopsies (p 4 0.31, Chi-square analysis).

The total bone area of the whole cross-section in thecontrol group showed that males had significantly morebone than females (males 227.55 ± 14.9 mm2; females 184.8± 6.83 mm2; p 4 0.015). Although total bone area waslower in samples from femoral neck fractures than femalecontrols, this was not significant (fractures 165.85 ± 10.08; p4 0.159). However, when the total amount of bone wasexpressed as a proportion of bone + marrow, it was signifi-cantly reduced in the fracture group (Tt.Ar: female fracture27.83 ± 1.18%, female control 33.62 ± 1.47%; p 4 0.0054;male control 30.81 ± 2.23). In the control group, there wereno differences in the Tt.Ar (%) between females and males(p 4 0.298). There were no differences in either the totalbone area or the Tt.Ar (%) between the complete andincomplete biopsies from the fracture group.

FIG. 1. Schematic cross-section of the femoral neck show-ing the eight regions used for the segmental analysis. Re-gions: I, inferior; I-A, inferoanterior; A, anterior; S-A, su-peroanterior; S, superior; S-P, superoposterior; P, posterior;and I-P, inferoposterior.

BELL ET AL.114

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S-P

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I-A

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Figure 1: Samples were divided into octants. Tensile is superior, superior-posterior (S, S-P). Compressive is inferior, inferior-anterior (I, I-A).

Figure 2: Dynamic histomorphometric indices presented as mean ± SEM. Matching letters denote significance with p<0.05.

model the cortical width data in the frequency domain.Modeling cortical widths takes account of the subject varia-tion, as well as location, biopsy type (i.e., fracture or con-trol), and gender. It was postulated that modeling in thefrequency domain would make it possible to mathemati-cally predict cortical widths at any location in the femoralneck. A model with fewer independent variates (i.e., fewerthan 128 separate width measurements) has equal orgreater power to achieve between-group separation at spe-cific locations within the femoral neck cortex.

The circumferential distribution of cortical widths in boththe control (male or female) and fracture (complete or in-complete) groups were modeled using the JMP statisticalpackage. To normalize the distribution of residuals, thesquare root of the cortical width (dependent variable) wasadopted. Least squares regression models used (1) a simpleFourier series, periodic functions of the measurement angle(sin angle + cos angle, sin 2� angle + cos 2� angle, sin 3�angle + cos 3� angle, sin 4� angle + cos 4� angle, sin 6�angle + cos 6� angle, sin 8� angle + cos 8� angle, sin 9�angle + cos 9� angle), or (2) the 128 width measurements asindependent categorical variables. For both models, subjectand gender or disease were used as independent categoricalvariables, and disease or gender were modeled as an inter-action with the angular location of width. Comparison ofthese two models demonstrated that the model with 128independent widths measurements improved the goodnessof fit, but because it increased the numbers of degrees of

freedom assigned to the model this improvement was notstatistically significant in the comparison for the effect ofgender (p 4 0.071) or for that of disease (p 4 0.94). Fromthe first (frequency domain) model the circumferential dis-tribution of cortical widths was predicted (with 95% confi-dence intervals [CIs]) for each subject group.

RESULTSSubjects

For the control subjects, there were no significant differ-ences between the males and females in their ages (p >0.75). Time since death was also unrelated to the amountsof cortical or cancellous bone (p > 0.21). There was nosignificant difference in the ages of the female fracture andfemale control groups (p > 0.21). In the female fracturegroup, there was no association between time since fractureand the amounts of cortical (p > 0.44) or cancellous bone (p> 0.93).

Total bone area

In the control samples, male subjects had a significantlygreater maximum (male 34.32 ± 0.79 mm, female 30.76 ±0.55; p 4 0.0016) and minimum (male 29.66 ± 1.13, female24.52 ± 0.61; p 4 0.0012) cross-section diameter. However,there were no differences in these dimensions between thefemale control and the female fracture group (fracture:maximum 31.67 ± 1.08, p 4 0.503; minimum 25.64 ± 0.72, p4 0.271). The ratio of maximum to minimum diameterswas not different between fractures and controls (fractures:1.25 ± 0.04; female controls 1.26 ± 0.03, male controls 1.16± 0.04; p > 0.05 Tukey–Kramer HSD test).Six of the 13 biopsies from the fracture cases had sub-

stantial proportions of the posterior and inferoposterior re-gions missing, with the other regions being intact. Therewere no differences in the maximum and minimum diam-eters between the complete and incomplete biopsies nor inthe ratio of these diameters (p > 0.635). The proportion ofsubcapital (n 4 5) and transcervical (n 4 1) fractures wasnot significantly different from that in the group of com-plete biopsies (p 4 0.31, Chi-square analysis).

The total bone area of the whole cross-section in thecontrol group showed that males had significantly morebone than females (males 227.55 ± 14.9 mm2; females 184.8± 6.83 mm2; p 4 0.015). Although total bone area waslower in samples from femoral neck fractures than femalecontrols, this was not significant (fractures 165.85 ± 10.08; p4 0.159). However, when the total amount of bone wasexpressed as a proportion of bone + marrow, it was signifi-cantly reduced in the fracture group (Tt.Ar: female fracture27.83 ± 1.18%, female control 33.62 ± 1.47%; p 4 0.0054;male control 30.81 ± 2.23). In the control group, there wereno differences in the Tt.Ar (%) between females and males(p 4 0.298). There were no differences in either the totalbone area or the Tt.Ar (%) between the complete andincomplete biopsies from the fracture group.

FIG. 1. Schematic cross-section of the femoral neck show-ing the eight regions used for the segmental analysis. Re-gions: I, inferior; I-A, inferoanterior; A, anterior; S-A, su-peroanterior; S, superior; S-P, superoposterior; P, posterior;and I-P, inferoposterior.

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Figure 1: Samples were divided into octants. Tensile is superior, superior-posterior (S, S-P). Compressive is inferior, inferior-anterior (I, I-A).

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model the cortical width data in the frequency domain.Modeling cortical widths takes account of the subject varia-tion, as well as location, biopsy type (i.e., fracture or con-trol), and gender. It was postulated that modeling in thefrequency domain would make it possible to mathemati-cally predict cortical widths at any location in the femoralneck. A model with fewer independent variates (i.e., fewerthan 128 separate width measurements) has equal orgreater power to achieve between-group separation at spe-cific locations within the femoral neck cortex.

The circumferential distribution of cortical widths in boththe control (male or female) and fracture (complete or in-complete) groups were modeled using the JMP statisticalpackage. To normalize the distribution of residuals, thesquare root of the cortical width (dependent variable) wasadopted. Least squares regression models used (1) a simpleFourier series, periodic functions of the measurement angle(sin angle + cos angle, sin 2� angle + cos 2� angle, sin 3�angle + cos 3� angle, sin 4� angle + cos 4� angle, sin 6�angle + cos 6� angle, sin 8� angle + cos 8� angle, sin 9�angle + cos 9� angle), or (2) the 128 width measurements asindependent categorical variables. For both models, subjectand gender or disease were used as independent categoricalvariables, and disease or gender were modeled as an inter-action with the angular location of width. Comparison ofthese two models demonstrated that the model with 128independent widths measurements improved the goodnessof fit, but because it increased the numbers of degrees of

freedom assigned to the model this improvement was notstatistically significant in the comparison for the effect ofgender (p 4 0.071) or for that of disease (p 4 0.94). Fromthe first (frequency domain) model the circumferential dis-tribution of cortical widths was predicted (with 95% confi-dence intervals [CIs]) for each subject group.

RESULTSSubjects

For the control subjects, there were no significant differ-ences between the males and females in their ages (p >0.75). Time since death was also unrelated to the amountsof cortical or cancellous bone (p > 0.21). There was nosignificant difference in the ages of the female fracture andfemale control groups (p > 0.21). In the female fracturegroup, there was no association between time since fractureand the amounts of cortical (p > 0.44) or cancellous bone (p> 0.93).

Total bone area

In the control samples, male subjects had a significantlygreater maximum (male 34.32 ± 0.79 mm, female 30.76 ±0.55; p 4 0.0016) and minimum (male 29.66 ± 1.13, female24.52 ± 0.61; p 4 0.0012) cross-section diameter. However,there were no differences in these dimensions between thefemale control and the female fracture group (fracture:maximum 31.67 ± 1.08, p 4 0.503; minimum 25.64 ± 0.72, p4 0.271). The ratio of maximum to minimum diameterswas not different between fractures and controls (fractures:1.25 ± 0.04; female controls 1.26 ± 0.03, male controls 1.16± 0.04; p > 0.05 Tukey–Kramer HSD test).Six of the 13 biopsies from the fracture cases had sub-

stantial proportions of the posterior and inferoposterior re-gions missing, with the other regions being intact. Therewere no differences in the maximum and minimum diam-eters between the complete and incomplete biopsies nor inthe ratio of these diameters (p > 0.635). The proportion ofsubcapital (n 4 5) and transcervical (n 4 1) fractures wasnot significantly different from that in the group of com-plete biopsies (p 4 0.31, Chi-square analysis).

The total bone area of the whole cross-section in thecontrol group showed that males had significantly morebone than females (males 227.55 ± 14.9 mm2; females 184.8± 6.83 mm2; p 4 0.015). Although total bone area waslower in samples from femoral neck fractures than femalecontrols, this was not significant (fractures 165.85 ± 10.08; p4 0.159). However, when the total amount of bone wasexpressed as a proportion of bone + marrow, it was signifi-cantly reduced in the fracture group (Tt.Ar: female fracture27.83 ± 1.18%, female control 33.62 ± 1.47%; p 4 0.0054;male control 30.81 ± 2.23). In the control group, there wereno differences in the Tt.Ar (%) between females and males(p 4 0.298). There were no differences in either the totalbone area or the Tt.Ar (%) between the complete andincomplete biopsies from the fracture group.

FIG. 1. Schematic cross-section of the femoral neck show-ing the eight regions used for the segmental analysis. Re-gions: I, inferior; I-A, inferoanterior; A, anterior; S-A, su-peroanterior; S, superior; S-P, superoposterior; P, posterior;and I-P, inferoposterior.

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ORS 2016 Annual Meeting Poster No. 0040